If $A=\begin{bmatrix}1&-2&3\\-4&2&5\end{bmatrix}$ and $B=\begin{bmatrix}2&3\\4&5\\2&1\end{bmatrix}$, then find the product AB and BA.
Answer & explanation
Correct answer: option 1
$AB=\begin{bmatrix}1&-2&3\\-4&2&5\end{bmatrix}\begin{bmatrix}2&3\\4&5\\2&1\end{bmatrix}$
$=\begin{bmatrix}2-8+6&-3-10+3\\-8+8+10&-12+10+5\end{bmatrix}$
$=\begin{bmatrix}0&-4\\10&3\end{bmatrix}$
$BA= \begin{bmatrix}2&3\\4&5\\2&1\end{bmatrix}\begin{bmatrix}1&-2&3\\-4&2&5\end{bmatrix}$
$=\begin{bmatrix}2-12&-4+6&6+15\\4-20&-8+10&12+25\\2-4&-4+2&6+5\end{bmatrix}$
$=\begin{bmatrix}-10&2&21\\-16&2&37\\-2&-2&11\end{bmatrix}$